I have been doing this for a while now(farming pets, and wanted to hit exalted), and I have to say it is one of the worst fights for us in there. Here is what I do to get them down. First off, clear all the trash so that you don't get punished by those adds rushing in to help the Emps. Now create a simple focus macro that you will use to to shoot LB, and keep flame shock up on the casting Emperor. Get your back to a wall or a corner, target the Emperor with the sword, and just melee him down. Your Lava Lash will do nothing to him, but your primary sources of damage will be Storm strike, Ascendance, and WF procs. This fight take a while but it is very doable. The biggest pains are getting knocked around, having the mobs "switch" on you and losing your melee target, and then the adds coming in if you didn't kill them.
pop ascendance lust stormlash fet and maybe a pot on the non magic immune one should be dead or close to dead
make sure you are in position (back to wall) and preferably just after a swap before you start bursting though
I have not soloed them as a enha, I did as a retri on 85 though, the problem is indeed the issue with one of them being physically immune and the other one magical, I just made macros with my specific abilities targetting the correct twin.
In your case it would be something like
/target Emperor Vek'nilash
Making macros for all of your abilities like that its np, then you just pull Vek'nilash into the corner next to the stairs hes standing on and as soon as they make the first switch both of them should be on top of eachother, spam your normal rotation and eventually they fall over, no decent dps should have problems nuking them harder then they heal especially with the 5.1 healing nerf.